# Asymptotic controllability implies feedback stabilization

@article{Clarke1997AsymptoticCI, title={Asymptotic controllability implies feedback stabilization}, author={Frank H. Clarke and Yu. S. Ledyaev and Eduardo Sontag and Andreĭ I. Subbotin}, journal={IEEE Trans. Autom. Control.}, year={1997}, volume={42}, pages={1394-1407} }

It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a smoothed version of a control-Lyapunov function, iteratively sending trajectories into smaller and smaller neighborhoods of a desired equilibrium. A major technical problem, and one of the contributions of the present paper, concerns the precise meaning of "solution" when using a discontinuous…

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